Time-dependent density-functional theory beyond the adiabatic approximation: insights from a two-electron model system

TL;DR

This paper investigates the limitations of the adiabatic approximation in time-dependent density-functional theory (TDDFT) using a two-electron model, revealing how nonadiabatic effects lead to dissipation and differ between finite and infinite systems.

Contribution

It provides a detailed analysis of nonadiabatic effects in TDDFT beyond ALDA using a two-electron model, highlighting the failure of nonadiabatic extensions in finite systems.

Findings

Dissipation arises from multiple particle-hole excitations.

Nonadiabatic extension of ALDA fails for finite systems.

Nonadiabatic extension becomes accurate in the thermodynamic limit.

Abstract

Most applications of time-dependent density-functional theory (TDDFT) use the adiabatic local-density approximation (ALDA) for the dynamical exchange-correlation potential Vxc(r,t). An exact (i.e., nonadiabatic) extension of the ground-state LDA into the dynamical regime leads to a Vxc(r,t) with a memory, which causes the electron dynamics to become dissipative. To illustrate and explain this nonadiabatic behavior, this paper studies the dynamics of two interacting electrons on a two-dimensional quantum strip of finite size, comparing TDDFT within and beyond the ALDA with numerical solutions of the two-electron time-dependent Schroedinger equation. It is shown explicitly how dissipation arises through multiple particle-hole excitations, and how the nonadiabatic extension of the ALDA fails for finite systems, but becomes correct in the thermodynamic limit.